2026 YTSS P1 Q22

In the diagram, \(ABCD\) is a parallelogram.

Diagonals \(AC\) and \(BD\) intersect at \(E\) and \(G\) is the midpoint of \(BE\).

\(F\) is a point of \(BC\) such that \(\overrightarrow{BC}=3\overrightarrow{BF}\).

It is given that \(\overrightarrow{BF}=\mathbf a\) and \(\overrightarrow{CE}=\mathbf b\).

1. Express each of the following vectors in terms of a and b as simply as possible.
   1. \(\overrightarrow{BA}\)[1]
   2. \(\overrightarrow{BD}\)[1]
   3. \(\overrightarrow{AG}\)[2]
2. Show that points \(A,G\) and \(F\) are collinear.[2]
3. Find the value of \(\dfrac{\text{area of}\hspace{0.5em}\triangle BFG}{\text{area of}\hspace{0.5em}ABCD}\).[2]